Point-wise Symmetry of Birkhoff-James Orthogonality and Geometry of \mathbbB(ℓ_∞ⁿ,ℓ₁^m)

2022/11/15 by Babhrubahan Bose, Bose, Babhrubahan
Engineering · Mathematics · #46A32 #FOS: Mathematics #Functional Analysis (math.FA) #Geometric and Algebraic Topology #Mathematics and Applications #Primary 46B20 #Secondary 46B28 #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2211.08455

openalex publication_date 2022/11/15 · openalex created_date 2022/11/25 · openalex updated_date 2026/07/28

Abstract

We study the relationship between the point-wise symmetry of Birkhoff-James orthogonality and the geometry of the space of operators \mathbbB(ℓ_∞ⁿ,ℓ₁^m). We show that any non-zero left-symmetric point in this space is a smooth point. We also show that for n≥4, any unit norm right-symmetric point of this space is an extreme point of the closed unit ball. This marks the first step towards characterizing the extreme points of these unit balls and finding the Grothendieck constants G(m,n) using Birkhoff-James orthogonality techniques.

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